It is known that every C·_(0)-contraction has a dilation to a Hardy shift.This leads to an elegant analytic functional model for C·_(0)-contractions,and has motivated lots of further works on the model theor...It is known that every C·_(0)-contraction has a dilation to a Hardy shift.This leads to an elegant analytic functional model for C·_(0)-contractions,and has motivated lots of further works on the model theory and generalizations to commuting tuples of C·_(0)-contractions.In this paper,we focus on doubly commuting sequences of C·_(0)-contractions,and establish the dilation theory and the analytic model theory for these sequences of operators.These results are applied to generalize the Beurling-Lax theorem and Jordan blocks in the multivariable operator theory to the operator theory in the infinite-variable setting.展开更多
The microstructures of Mg96.17Zn3.15Y0.50Zr0.18 alloys solidified under 2-6 GPa high pressure were investigated by employing SEM(EDS) and TEM.The strengthening mechanism of experimental alloy solidified under high pre...The microstructures of Mg96.17Zn3.15Y0.50Zr0.18 alloys solidified under 2-6 GPa high pressure were investigated by employing SEM(EDS) and TEM.The strengthening mechanism of experimental alloy solidified under high pressure is also discussed by analyzing the compressive properties and compression fracture morphology.The results show that the microstructure of experimental alloy becomes significantly fine-grained with increasing GPa level high pressure during solidification process,and the secondary dendrite arm spacing reduces from 40 μm at atmospheric pressure to 10 μm at 6 GPa pressure.The morphology of the second phases changes from the net structure by the lamellar-type eutectic structure at atmospheric pressure to discontinuous thin rods or particles at 6 GPa pressure.Besides,the solid solubility of Zn in the Mg matrix is improved with the increase of the solidification pressure.Compared with atmospheric-pressure solidification,high-pressure solidification can improve the strength of the experimental alloy.The compressive stre ngth is improved from 263 to 437 MPa at 6 GPa.The fracture mechanism of the experimental alloy changes from cleavage fracture at atmospheric pressure to quasi-cleavage fracture at high pressure.The main mechanism of the strength improvement of the experimental alloy includes the grain refinement strengthening caused by the refinement of the solidification microstructure,the second phase strengthening caused by the improvement of the morphology and distribution of the second phases,and solid solution strengthening caused by the increase of the solid solubility of Zn in the Mg matrix.展开更多
A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, w...A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11871157 and 12101428)。
文摘It is known that every C·_(0)-contraction has a dilation to a Hardy shift.This leads to an elegant analytic functional model for C·_(0)-contractions,and has motivated lots of further works on the model theory and generalizations to commuting tuples of C·_(0)-contractions.In this paper,we focus on doubly commuting sequences of C·_(0)-contractions,and establish the dilation theory and the analytic model theory for these sequences of operators.These results are applied to generalize the Beurling-Lax theorem and Jordan blocks in the multivariable operator theory to the operator theory in the infinite-variable setting.
基金the National Natural Science Foundation of China(51675092,51775099)the Natural Science Foundation of Hebei Province(E2018501032,E2018501033)。
文摘The microstructures of Mg96.17Zn3.15Y0.50Zr0.18 alloys solidified under 2-6 GPa high pressure were investigated by employing SEM(EDS) and TEM.The strengthening mechanism of experimental alloy solidified under high pressure is also discussed by analyzing the compressive properties and compression fracture morphology.The results show that the microstructure of experimental alloy becomes significantly fine-grained with increasing GPa level high pressure during solidification process,and the secondary dendrite arm spacing reduces from 40 μm at atmospheric pressure to 10 μm at 6 GPa pressure.The morphology of the second phases changes from the net structure by the lamellar-type eutectic structure at atmospheric pressure to discontinuous thin rods or particles at 6 GPa pressure.Besides,the solid solubility of Zn in the Mg matrix is improved with the increase of the solidification pressure.Compared with atmospheric-pressure solidification,high-pressure solidification can improve the strength of the experimental alloy.The compressive stre ngth is improved from 263 to 437 MPa at 6 GPa.The fracture mechanism of the experimental alloy changes from cleavage fracture at atmospheric pressure to quasi-cleavage fracture at high pressure.The main mechanism of the strength improvement of the experimental alloy includes the grain refinement strengthening caused by the refinement of the solidification microstructure,the second phase strengthening caused by the improvement of the morphology and distribution of the second phases,and solid solution strengthening caused by the increase of the solid solubility of Zn in the Mg matrix.
文摘A new C~* -algebra E+E_* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra of B (H^2) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.
